Monitoring A Kinematically Redundant Robot

ABSTRACT

A method for monitoring a kinematically redundant robot includes detecting joint forces acting in the joints of the robot, determining an external work force between a robot-permanent reference point and an environment based on the detected joint forces, determining a further monitoring variable that is at least substantially independent of an external force acting on the robot-permanent reference point based on the detected joint forces, and monitoring the determined external work force and the determined further monitoring variable.

CROSS-REFERENCE

This application claims the benefit of German Patent Application No. 102013 010 290.1 (pending), filed Jun. 19, 2013, the disclosure of whichis incorporated by reference herein in its entirety.

TECHNICAL FIELD

The present invention relates to a method for monitoring a kinematicallyredundant robot, and a robot having a control means and a computerprogram product having a programming code for executing a method of thistype.

BACKGROUND

Robots can exert forces on their environment—for example, in joiningoperations—or unintentionally as well—in a collision forexample—wherein, for a more compact design, anti-parallel pairs offorces are also present, i.e. torques, that in general are referred toas forces.

According to operating parameters, it is thus known to detect jointforces nand to evaluate model-based externally induced joint forces{circumflex over (T)}_(e) that result in the joints by a contact of therobot with the environment.

With kinematically redundant robots, working forces {circumflex over(f)}_(w) in the workspace between a robot-permanent reference point, inparticular the TCP (Tool Center Point) of the robot, and theenvironment, can be evaluated and monitored based on these joint forces,in particular by means of a so-called pseudoinverse of the transposedJacobian matrix (J^(T))^(#):

{circumflex over (f)} _(W)=(J ^(T))^(#) ·{circumflex over (T)} _(e)

If the working force evaluated in this manner exceeds a threshold valueat the TCP, a safety reaction is triggered, such that the robot is shutdown, or moved back, for example.

In particular, measurement and modeling inaccuracies, which act on thepseudoinverse (J^(T))^(#) can lead thereby to errors for the evaluatedworking force {circumflex over (f)}_(W) at the robot-permanent referencepoint. Additionally, or alternatively, joint torques can be projectederroneously on a fictitious working force {circumflex over (f)}_(W)acting on the TCP, due to contact forces acting on a point on the robotspaced apart from the TCP. In particular, if the joint forces resultingfrom this contact force spaced apart from the TCP are substantiallylocated in the null space of the pseudoinverse of the transposedJacobian matrix, then a quantitatively very small working force isevaluated and no safety reaction is triggered.

SUMMARY

The object of the present invention is to improve the operation of thekinematically redundant robot, in particular to reduce at least some ofthe disadvantages discussed above.

According to one aspect of the present invention, a kinematicallyredundant robot is monitored. A kinematically redundant robot isunderstood in the present context to be, in particular, a robot having areference point permanently allocated thereto, in particular, a tool(flange) coordinate system, or TCP (“Tool Center Point”), the Jacobianmatrix J of which is not quadratic and/or does not have a complete rank,wherein the Jacobian matrix is defined in the standard format as amatrix for the partial derivation of the position or speed of thereference point x, permanently allocated to the robot, in the workspaceaccording to the minimum, in particular, joint coordinates, or speeds,in particular joint angles, of the robot:

$\frac{x}{t} = {{\frac{\partial x}{\partial q} \cdot \frac{q}{t}} = {{J(q)}\frac{q}{t}}}$

Because the speed of the robot-permanent reference point has a maximumof three Cartesian, or translation, speeds, and three angular, orrotational, speeds (dim(x)≦6), a robot having seven or more joints(dim(q)≧7), in particular, is kinematically redundant. A robot havingsix or less joints can also be kinematically redundant if, for example,only the translation speeds of the robot-permanent reference point aretaken into account, or, respectively, no rotational speeds are takeninto account at the robot-permanent reference point.

In one embodiment, joint forces, in particular joint torques, which acton the joints of the robot, are detected, in particular by means of adetection means. The detection means can have one or more force sensors,in particular torque sensors, in a further development, which aredisposed on one or more, preferably all, joint axes, in particular driveaxes of joint drives for the robot. Additionally, or alternatively,motor currents for the joint drive and/or joint accelerations, can bedetected, in particular by means of the detection means, and from this,joint forces, in particular joint torques, can be detected, inparticular, evaluated.

Based on the detected joint forces, an external working force in theworkspace, between a robot-permanent reference point and an environmentof the robot, in particular a force to the TCP, is determined, inparticular by means of a processing means.

For this, model based externally induced joint forces are evaluated, inone embodiment, based on the detected joint forces, by way of example,via a disturbance variable observer, or in that drive, tractive,gravitational, frictional, and/or similar, joint force componentsbelonging to the robot are subtracted from the detected joint forces. Ifthe robot is modeled in the standard manner by means of the movementequation

${{{M(q)} \cdot \frac{^{2}q}{t^{2}}} - {h\left( {q,\frac{q}{t}} \right)}} = T$

having the mass matrix M and the joint forces τ, the externally inducedjoint force {circumflex over (T)}_(e) occurring in the joints throughcontact with the environment can be evaluated when the minimumcoordinates for q are known. The detected, or determined by this means,externally induced joint forces are mapped, in one embodiment, by meansof a linear mapping, in particular a pseudoinverse of a transposedJacobian matrix for the robot-permanent reference point, onto theexternal working force:

{circumflex over (f)} _(W)=(J ^(T))^(#) ·{circumflex over (T)} _(e)

The pseudoinverse of a (transposed) Jacobian matrix can, in particular,be defined in a standard format by means of

J ^(#) =A ⁻¹ ·J ^(T)·(J·A ⁻¹ ·J ^(T))⁻¹ or

(J ^(T))^(#) =A ⁻¹ ·J·(J ^(T) ·A ⁻¹ ·J)⁻¹

with the weighting matrix A. This is the identity matrix in oneembodiment, such that the pseudoinverse is the Moore-Penrosepseudoinverse. In another embodiment, the weighting matrix A is the massmatrix M for the robot.

Likewise, the external working force can also be determined by othermeans, based on the detected joint forces, for example, by measuring andstoring pairs of detected, or determined by this means, externallyinduced joint forces and corresponding working forces and interpolationof these stored pairs for currently detected or determined joint forces.

In addition to the external working force, a further monitoringvariable, which—at least substantially—is independent of an externalforce acting on the robot-permanent reference point, is then determined,according to one aspect of the present invention, based on the detected,or determined by this means, externally induced joint forces. Thisfurther monitoring variable can, in particular, depend on an externalforce, exerted on the environment, or experienced, respectively, by therobot at a point spaced apart from the robot-permanent reference point,in particular at a link or joint.

When the robot intentionally makes contact with the environment by meansof the robot-permanent reference point, or, respectively, a force occurson the robot-permanent reference point in the workspace, the furthermonitoring variable in one embodiment is, at least substantially, equalto zero, in particular with respect to model and/or measurementinaccuracies. Accordingly, it is possible to detect that the robot hasmade contact with the environment, in particular an obstacle, with asurface spaced apart from the robot-permanent reference point by meansof a, in particular, significant, or sufficiently large, furthermonitoring variable. With model errors in the determination of theexternal working force, it is likewise possible that portions result,which affect the further monitoring variable. Accordingly, in additionto, or alternatively to, detecting an environment contact at a pointspaced apart from the robot-permanent reference point, a modelinginaccuracy can also be identified, which leads to an incorrectdetermination of the external working force. Thus, in addition to, oralternatively to, detecting an environment contact at a point spacedapart from the robot-permanent reference point, the plausibility of thedetermination of the external working force can be checked.

In one embodiment, this further monitoring variable corresponds to anexternal force at a point spaced apart from the robot-permanentreference point. For this reason, it shall also be referred to below asa crushing force, without this designation being intended to limit theother external forces in any way. This crushing force can be determinedin a manner analogous to that for the working force, in particular bymeans of measuring and storing pairs of joint forces and correspondingcrushing forces, and the interpolation of these stored pairs for currentjoint forces, or by mapping the detected, or determined by this means,externally induced joint forces onto the external crushing force, bymeans of a pseudoinverse of a transposed Jacobian matrix for a robotsurface spaced apart from the robot-permanent reference point, inparticular a link or a joint.

In one embodiment, the further monitoring variable can be determined bymultiplication of the joint forces with a null space projection operatorof the pseudoinverse of the transposed Jacobian matrix for therobot-permanent reference point. The null space projection operator of apseudoinverse of a transposed Jacobian matrix can be defined, inparticular in the standard format, by

B=└I−J ^(T)·(J ^(T))^(#)┘

with the identity matrix I. In other words, the portion of the detected,or determined by this means, externally induced joint forces is used asthe further monitoring variable in one embodiment, which by means of thepseudoinverse of the transposed Jacobian matrix is mapped for zero:

{circumflex over (f)} _(W)=(J ^(T))^(#)·{circumflex over (τ)}_(e)

{circumflex over (τ)}_(NS) =[I−J ^(T)·(J ^(T))^(#)]·{circumflex over(τ)}_(e)

This can also be physically reproduced: with a kinematically redundantrobot, the minimum coordinates are mapped, or permanently clearlyestablished, unambiguously at a position, in particular the positionand/or orientation, of a robot-permanent reference point, or a robotsurface spaced apart therefrom, respectively. Conversely, differentminimum coordinates exist, however, for a position. Accordingly,external working forces at the robot-permanent reference point, inparticular the TCP, are, in fact, clearly mapped for joint forces, inparticular externally induced joint forces. Conversely, joint forces, inparticular externally induced joint forces, may occur, however,corresponding to external crushing forces, which act, not on therobot-permanent reference point, but rather, on the robot surface spacedapart therefrom. Joint forces of this type can be partially or entirelyhidden, or projected into the null space of this linear mapping, in themapping of the joint forces onto the external working force, inparticular through the pseudoinverse of the transposed Jacobian matrix.Accordingly, in one embodiment of the present invention, the null spaceportion of this linear mapping, in general, a mapping of detected, ordetermined by this means, externally induced joint forces, is monitored.By means of this monitoring variable, an (additional) contact with theenvironment by the redundant robot can be detected and/or a plausibilityof the determined external working force can be checked.

Accordingly, in one embodiment, particularly by means of a monitoringmeans, the determined external work force and the further monitoringvariable, in particular the determined external crushing force and/orthe null space portion of the joint forces, in particular externallyinduced joint forces, are monitored and a safety reaction is triggeredwhen the determined external work force or the further monitoringvariable fulfill a monitoring condition. A force or a monitoringvariable can, in one embodiment, fulfill a monitoring condition if anorm, in particular a quantitative or maximum norm, exceeds the force,or monitoring variable, respectively, or a portion thereof, inparticular a sub-vector of the force, or monitoring variable,respectively, exceeds or falls below a given threshold value, inparticular if a quantity of the work force, or monitoring variable,respectively, or a maximum component of the work force, or themonitoring variable, respectively, exceeds or falls below a giventhreshold value. By way of example, a work force can be divided into onesub-vector, corresponding to a physical one, two, or three dimensionalforce, and one sub-vector corresponding to a one, two, or threedimensional torque. These two sub-vectors, the quantities, maximumcomponents, or suchlike, thereof, for example, can then be monitoredrespectively. The same applies to the further monitoring variable.

The monitoring conditions for the work force and for the furthermonitoring variable can be identical. Likewise, another monitoringcondition can be provided for the further monitoring variable. Inparticular, it may be convenient to limit the monitoring variable morestrongly than acceptable work forces, which are necessary for joining,for example. Accordingly, in one embodiment, a given threshold for thefurther monitoring variable is lower than for the work force.

The monitoring condition for the work force and/or the furthermonitoring variable can be defined such that they can be varied in oneembodiment. In particular, a given threshold value for the furthermonitoring variable and/or the work force can be such that it can beparameterized.

If the determined external work force fulfills the given monitoringcondition, a safety reaction is triggered, preferably a STOP 0, a STOP1, or a STOP 2, or a retreating movement of the robot. If the determinedfurther monitoring variable fulfills the given monitoring condition, thesame safety reaction can be triggered as that triggered when themonitoring condition for the work force has been fulfilled. Likewise, asafety reaction differing from that for the work force can be triggeredif the determined further monitoring variable fulfills the givenmonitoring condition, in particular a higher level STOP (such as a STOP0 for the further monitoring variable, as opposed to a STOP 1 for thework force), or an evasive movement, in particular a reorientation canbe triggered, while maintaining a position of the robot-permanentreference point.

According to one aspect of the present invention, a robot has a controlmeans, which is configured for executing a method described herein.According to one aspect, a computer program product, in particular acomputer readable storage medium, has a program code, which isconfigured for executing a method described herein, when the program isexecuted by a control means for the robot.

A means, as meant in the present invention, can be designed as hardwareand/or software, in particular a digital data processing unit, inparticular a microprocessor unit (CPU), preferably connected to astorage unit and/or a bus system, and/or having one or more programs orprogram modules. The CPU can be designed to process commands, which areimplemented in the form of a program installed in a storage system, todetect input signals from a data bus, and/or to issue output signals toa data bus. A storage system can have one or more, in particulardifferent, storage mediums, in particular optical, magnetic, solid stateand/or other non-volatile mediums. The program can be created such thatit embodies the procedures described herein, or is capable of executingsaid procedures, respectively, such that the CPU executes the steps ofsuch procedures, and thus, in particular, can monitor the robot.

One embodiment of the present invention can be illustrated as follows:with a kinematically redundant robot, joint forces, in particularexternally induced joint forces, on one hand, are mapped onto anexternal work force that acts on a robot-permanent reference point, inparticular a TCP. This external work force is monitored, and uponexceeding a given threshold, triggers a safety reaction.

With this mapping, in one embodiment, seven or more joint forces of therobot having seven or more axes are mapped onto a maximum of sixcomponents of the external work force (three components of a continuousforce vector and three components of a discontinuous torque vector).Consequently—due to the mapping via the pseudoinverse—not all of theinformation pertaining to the joint forces is made use of. Instead,joint forces resulting from an external crushing force are hidden bythis mapping.

For this reason, in one embodiment, the joint forces, in particular theexternally induced joint forces, on the other hand, are mapped onto afurther monitoring variable, which—at least substantially—is independentof an external force acting on the robot-permanent reference point. Thisfurther monitoring variable also triggers a safety reaction when a giventhreshold value has been exceeded. If, in a further development, thenull space projection operator for the mapping onto the work force isused for the mapping of the further monitoring variable, then the hiddennull space portion of the joint forces, i.e. the previously unusedinformation from the joint forces, is made use of. Because both externalcrushing forces, which have no, or very little, effect on the TCP, aswell as modeling inaccuracies that effect a further monitoring variabledetermined in this manner, can be used to check the plausibility of thedetermined work force, in particular, the accuracy of this fundamentalmodeling, and additionally, or alternatively, an external crushingforce, with which the redundant robot can crush an obstacle, can bechecked.

In general, according to one aspect of the present invention, a furthermonitoring variable is determined, based on joint forces that can alsooccur at a robot-permanent reference point, which, at leastsubstantially, is not subjected to forces, or can occur without anexternal work force being applied to the robot-permanent referencepoint, respectively. If this further monitoring variable exceeds a giventhreshold value, a safety reaction is triggered.

BRIEF DESCRIPTION OF THE FIGURES

Further advantages and features can be derived from the dependent claimsand the embodiment examples. For this, shown are, in part schematically:

FIG. 1: a robot according to one embodiment of the present invention;and

FIG. 2: a method according to one embodiment of the present invention.

DETAILED DESCRIPTION

FIG. 1 shows a kinematically redundant seven-axis lightweight robot 1according to one embodiment of the present invention, having sevenjoints, exhibiting the joint angles q₁−q₇=q, a TCP on a tool (flange)and a control means 2, which executes a process according to oneembodiment of the present invention, which shall be explained in greaterdetail below with reference to FIG. 2.

In a step S10, joint torques τ₁−τ₇=τ are detected by means of jointtorque sensors 1.1-1.7 of a detection means in the control means 2 fordetecting joint forces. From these, in a step S20, model-basedexternally induced joint forces {circumflex over (T)}_(e) are evaluatedby a processing means 2.1 in the control means 2, in that tractive,gravitational, drive, and similar, robot-internal components aresubtracted from the detected joint forces τ.

In a step S30, the externally induced joint forces {circumflex over(T)}_(e) determined in this manner are mapped on the external work forceby multiplication with the pseudoinverse of the transposed Jacobianmatrix of the TCP weighted with the mass matrix M of the robot 1:

{circumflex over (f)}_(W)=(J ^(T))^(#) ·{circumflex over (T)} _(e)

In a step S40, a further monitoring variable is determined in advance,parallel to, or subsequently, by means of the processing means, from theexternally induced joint forces {circumflex over (T)}_(e) bymultiplication with the null space projection operator of thistransposed Jacobian matrix:

{circumflex over (τ)}_(NS) =└I−J ^(T)·(J ^(T))^(#)┘·{circumflex over(τ)}_(e)

In steps S50, S60, a monitoring of whether a quantity for the work force(step S50) or the further monitoring variable (step S60) exceeds a giventhreshold value f₁ or f₂, respectively, is carried out by means of amonitoring means 2.2 in the control means 2. If this is the case (“Y” instep S50, or S60, respectively), a STOP 1 (when the threshold value f₁is exceeded by the work force), or a STOP 0 (when the threshold value f₂is exceeded by the further monitoring variable), is triggered.Processing and monitoring means can be implemented, in particular, by acomputer configured accordingly in terms of its programming.

LIST OF REFERENCE SYMBOLS

-   1 redundant robot-   1.1-1.7 joint force sensors (detection means)-   2 control means-   2.1 processing means-   2.2 monitoring means-   q₁-q₇ joint angles (minimum coordinates)-   TCP Tool Center Point (robot-permanent reference point)

What is claimed is:
 1. A method for monitoring a kinematically redundantrobot, the method comprising: detecting joint forces acting in joints ofthe robot; determining an external work force between a robot-permanentreference point and an environment based on the detected joint forces;determining, based on the detected joint forces, a further monitoringvariable which is at least substantially independent of an externalforce acting on the robot-permanent reference point; and monitoring thedetermined external work force and the determined further monitoringvariable.
 2. The method of claim 1, further comprising: triggering afirst safety reaction when the determined external work force fulfills afirst variably definable monitoring condition; and triggering the firstsafety reaction or a second safety reaction when the determined furthermonitoring variable fulfills the first monitoring condition or a secondpre-definable monitoring condition.
 3. The method of claim 1, whereinthe further monitoring variable comprises an external force spaced apartfrom the robot-permanent reference point.
 4. The method of claim 2,wherein the further monitoring variable comprises an external forcespaced apart from the robot-permanent reference point.
 5. The method ofclaim 1, wherein the joint forces are mapped onto the external workforce by a first linear mapping.
 6. The method of claim 2, wherein thejoint forces are mapped onto the external work force by a first linearmapping.
 7. The method of claim 3, wherein the joint forces are mappedonto the external work force by a first linear mapping.
 8. The method ofclaim 4, wherein the joint forces are mapped onto the external workforce by a first linear mapping.
 9. The method of claim 5, wherein thefirst linear mapping is a pseudoinverse of a transposed Jacobian matrixfor the robot-permanent reference point.
 10. The method of claim 6,wherein the first linear mapping is a pseudoinverse of a transposedJacobian matrix for the robot-permanent reference point.
 11. The methodof claim 7, wherein the first linear mapping is a pseudoinverse of atransposed Jacobian matrix for the robot-permanent reference point. 12.The method of claim 8, wherein the first linear mapping is apseudoinverse of a transposed Jacobian matrix for the robot-permanentreference point.
 13. The method of claim 9, wherein the same jointforces are mapped onto the further monitoring variable by a secondlinear mapping.
 14. The method of claim 10, wherein the same jointforces are mapped onto the further monitoring variable by a secondlinear mapping.
 15. The method of claim 11, wherein the same jointforces are mapped onto the further monitoring variable by a secondlinear mapping.
 16. The method of claim 12, wherein the same jointforces are mapped onto the further monitoring variable by a secondlinear mapping.
 17. The method of claim 13, wherein the second linearmapping is a null space projection operator of the pseudoinverse of thetransposed Jacobian matrix for the robot-permanent reference point. 18.A robot, comprising: a plurality of joints; and a control configured forexecuting the method of claim 1, the control comprising: a detectionmeans for detecting joint forces, a processing means for determining theexternal work force and further monitoring variable, and a monitoringmeans for monitoring the determined external work force and thedetermined further monitoring variable.
 19. The robot of claim 18,comprising at least seven joints.
 20. A computer program product,comprising: a non-transitory computer readable storage medium; and aprogram stored on the non-transitory computer readable storage mediumthat, when executed by a processing unit, causes the processing unit to:detect joint forces acting in joints of a kinematically redundant robot,determine an external work force between a robot-permanent referencepoint and an environment based on the detected joint forces, determine,based on the detected joint forces, a further monitoring variable whichis at least substantially independent of an external force acting on therobot-permanent reference point, and monitor the determined externalwork force and the determined further monitoring variable.